Natasha Blucher, the advocate for the baby known as "Asha" and her family, said she was worried the one-year-old's removal could be imminent.

The Darwin Asylum Seeker Support and Advocacy Network advocacy coordinator said Serco guards had blocked all calls to their room at Brisbane's Lady Cilento Hospital and immigration officers had warned the baby would be moved on Saturday.

However, a Children's Health Queensland spokesman said there had been no change to baby Asha's position.

The Department of Immigration and Border Protection has been contacted for comment.

An estimated crowd of more than 300 protesters was warned to remain calm if baby Asha emerged.

The crowd split into three groups to guard all exits from the hospital.

Horns were honking in support almost non-stop as cars passed through the busy intersection outside the hospital.

Ms Blucher said a hospital doctor had assured the family she wouldn't be going anywhere but the combination of factors was "concerning".

"I deal with a lot of transfers between detention centres and offshore, it's always the practice to remove the person from the compound normally and then hold them incommunicado," she said.

"So they're not allowed to call their lawyers, their lawyers aren't allowed to call them.

"They're not allowed to call their support people or tell any friends where they are, and then they get transferred after that.

"My concern is because they're holding her incommunicado, it could be part of that transfer process but it could also be just to deny her the right to speak to people who are providing support to her."

On Thursday, Immigration Minister Peter Dutton warned he would not be "pressured" over the issue.

"If people have received medical assistance and the ­assistance is no longer required, if they've recovered from their medical condition, then they'll be returned to Nauru," he told 4BC radio.

Human Rights Law Centre lawyers earlier in the week announced they'd received an undertaking a 72-hour warning would be given before Asha was moved, even as they raised fears the government was planning to revoke the warning period for 266 other asylum seekers.